Revised and Generalized Results of Averaging Principles for the Fractional Case
[ X ]
Tarih
2024
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Mdpi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
The averaging principle involves approximating the original system with a simpler system whose behavior can be analyzed more easily. Recently, numerous scholars have begun exploring averaging principles for fractional stochastic differential equations. However, many previous studies incorrectly defined the standard form of these equations by placing epsilon in front of the drift term and epsilon in front of the diffusion term. This mistake results in incorrect estimates of the convergence rate. In this research work, we explain the correct process for determining the standard form for the fractional case, and we also generalize the result of the averaging principle and the existence and uniqueness of solutions to fractional stochastic delay differential equations in two significant ways. First, we establish the result in Lp space, generalizing the case of p=2. Second, we establish the result using the Caputo-Katugampola operator, which generalizes the results of the Caputo and Caputo-Hadamard derivatives.
Açıklama
Anahtar Kelimeler
generalized fractional operator, stochastic fractional differential equations, existence and uniqueness
Kaynak
Axioms
WoS Q Değeri
N/A
Scopus Q Değeri
Cilt
13
Sayı
11
